In the IS-MP model we have real interest rate on the vertical axis and outputon the horizontal axis. Explain the IS curve, and its slope by assuming aclosed economy where 𝐶 = 𝐶0 + 𝑐(𝑌 − 𝑇), 𝐼 = 𝐼0 − 𝑏𝑟 and 𝐺 = 𝐺0. 𝐼0 and 𝐺0and 𝐶0 are all positive, 𝑏 > 0 and 0 < 𝑐 < 1. 𝑇 is a lump sum tax.
Question
In the IS-MP model we have real interest rate on the vertical axis and outputon the horizontal axis. Explain the IS curve, and its slope by assuming aclosed economy where 𝐶 = 𝐶0 + 𝑐(𝑌 − 𝑇), 𝐼 = 𝐼0 − 𝑏𝑟 and 𝐺 = 𝐺0. 𝐼0 and 𝐺0and 𝐶0 are all positive, 𝑏 > 0 and 0 < 𝑐 < 1. 𝑇 is a lump sum tax.
Solution
The IS curve (Investment-Savings curve) in the IS-MP model represents the relationship between the real interest rate and the level of income (output) in the economy that is in equilibrium in the goods market.
The IS curve is derived from the equilibrium condition for the goods market, which is that the total supply of goods (output, Y) must equal the total demand for goods, which is the sum of consumption (C), investment (I), and government spending (G).
Given the equations for C, I, and G in the question, we can write the goods market equilibrium condition as follows:
Y = C0 + c(Y - T) + I0 - br + G0
We can solve this equation for Y to find the level of output that will achieve goods market equilibrium for any given real interest rate r.
The slope of the IS curve is determined by the parameters c and b in the consumption and investment equations. The slope of the IS curve is negative because an increase in the real interest rate reduces investment (since the cost of borrowing to finance investment is higher), which reduces the demand for goods and hence reduces the equilibrium level of output.
The parameter c in the consumption equation represents the marginal propensity to consume out of disposable income (income after tax). A higher value of c means that consumers spend a larger proportion of their disposable income, which increases the demand for goods and hence increases the equilibrium level of output for any given real interest rate.
The parameter b in the investment equation represents the sensitivity of investment to the real interest rate. A higher value of b means that investment is more sensitive to changes in the real interest rate, which makes the IS curve steeper (since a given change in the real interest rate has a larger effect on investment and hence on the equilibrium level of output).
In summary, the IS curve shows the negative relationship between the real interest rate and the level of output that achieves goods market equilibrium, and its slope is determined by the marginal propensity to consume and the sensitivity of investment to the real interest rate.
Similar Questions
Consider the IS relation for an economy with both government and external sectors. Which of the following statements is correct?Group of answer choicesA rise in the marginal tax rate combined with a fall in the responsiveness of investment to the rate of interest might reduce, or it might increase or it might leave unchanged the slope of IS curve.An increase in the marginal propensity to import should lead to a parallel shift to the left in the IS curve.A rise in the marginal propensity to consume together with a rise in exogenous taxation should shift the IS curve leftwards as well as making it flatter.An increase in the income-expenditure multiplier combined with a reduction in the responsiveness of investment to the rate of interest would definitely make the IS curve flatter.
Which of the following statements is correct ?Group of answer choicesThe IS relation refers to combinations of real income and the rate of interest consistent with equilibrium in the money market.Points on the IS curve shows how aggregate expenditure varies with the rate of interest when the goods market is not in equilibrium.The slope of the IS curve reflects the sensitivity of consumption and investment to changes in the rate of interest as well as the size of the multiplier.An increase in the marginal propensity to consume would result in a parallel rightward shift of the IS curve.
In the IS-LM model with interest setting monetary policy and endogenous money, the LM curve is horizontal becauseGroup of answer choicesthe transactions demand for money adjusts to the speculative demand for money through the establishment of the rate of interestdemand for money adjusts to supply of money through the establishment of an equilibrium level of incomedemand for and supply of money brought into equilibrium through the establishment of rate of interestthe quantity of money adjusts to the demand for money for a given policy determined rate of interest
The IS curve is downward-sloping because goods market equilibrium implies that an increase in taxes leads to a lower level of outputGroup of answer choicesTrueFalse
Consider a different version of the Taylor rule, where monetary policy depends onlyon short-run output: − = ea) Draw an IS-MP diagram, but instead of the usual MP curve, plot the simplifiedversion of the Taylor rule. You might label this curve MPR for “monetarypolicy rule”.b) Now consider the effect of a positive aggregate demand shock in the IS-MPRdiagram. (An example might be a fiscal stimulus.) Compare and contrast theeffect of this shock on the economy in the standard IS-MP diagram versus theIS-MPR diagram. Why is the result different?c) Economists refer to the result in the IS-MPR diagram as “crowding out”. Whatgets crowded out and why?
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